Knife Tool is stuck to the origin of the geometry of the object
Your View clipping range in the 3D View in the 'bad' file, is enormous, so the depth calculation for point-picking in the viewport is beyond floating-point resolution.
In the 'View' tab of the N sidebar, set the Clip Start and Clip End to values that are enough to comfortably accommodate your scene, but no more.
A visual clue that this is happening is 'shards' appearing in shaded surfaces, like Z-fighting, even though the surfaces interfering with one another are not coincident.